To find the graph of the first and the second function, let's substitute x by 1 and find the function that has the corresponding y value.
a)
[tex]\begin{gathered} f(x)=2^x \\ f(1)=2^1 \\ f(1)=2 \end{gathered}[/tex]
The graph that has the point (1, 2) is the green graph.
b)
[tex]\begin{gathered} f(x)=3^x \\ f(1)=3^1 \\ f(1)=3 \end{gathered}[/tex]
The graph that has the point (1, 3) is the yellow graph.
To find the graph of the third and the fourth function, let's substitute x by -1 and find the function that has the corresponding y value.
c)
[tex]\begin{gathered} f(x)=(\frac{1}{2})^x \\ f(-1)=(\frac{1}{2})^{-1} \\ f(-1)=(\frac{2}{1})^1 \\ f(-1)=2 \end{gathered}[/tex]
The graph that has the point (-1, 2) is the blue graph.
d)
[tex]\begin{gathered} f(x)=(\frac{1}{3})^x \\ f(-1)=(\frac{1}{3})^{-1} \\ f(-1)=(\frac{3}{1})^1 \\ f(-1)=3 \end{gathered}[/tex]
The graph that has the point (-1, 3) is the red graph.
Answer:
[tex]\begin{gathered} f(x)=2^x\Rightarrow g \\ f(x)=3^x\operatorname{\Rightarrow}y \\ f(x)=(\frac{1}{2})^x\operatorname{\Rightarrow}b \\ f(x)=(\frac{1}{3})^x\operatorname{\Rightarrow}r \end{gathered}[/tex]
